Question 42056
Let the distance between Townsville and Goanna Creek = x km.


For first bus:
Distance to be traveled = x km.
Average speed = 50 km/h.
Therefore, time taken = {{{DISTANCE/SPEED}}} = {{{x/50}}} hours.


For second bus:
Distance to be traveled = x km.
Average speed = 70 km/h.
Therefore, time taken = {{{DISTANCE/SPEED}}} = {{{x/70}}} hours.


The second bus started 2 hrs. after the departure of the first bus but both reached the destination at the same time.
So, the second bus takes 2 hr. less time than the first bus to complete the journey.


So we can write,
(Time taken by second bus in hrs.) = (Time taken by first bus in hrs.) - 2
or {{{x/70 = x/50 - 2}}}
or {{{x/50 - x/70 = 2}}}
or {{{(70x-50x)/(50*70) = 2}}}
or {{{20x/(70*50) = 2}}}
or {{{x/(7*50) = 1}}}
or x = 350


Hence, the reqd. distance is 350 km.